In a first aspect the present invention relates to an X-ray diffraction method of mapping grain structures in a crystalline material sample, where an X-ray source provides a polychromatic X-ray beam in a beam path, in which beam path the polychromatic X-ray beam is divergent, a staging device positions the crystalline material sample in the beam path, and an X-ray detector detects a plurality of diffracted X-ray beams leaving the crystalline material sample.
The article “A focusing Laue diffractometer for investigation of bulk crystals” by Matthias Stockmeier and Andreas Magerl, Journal of Applied Crystallography (2008), 41, 754-760, describes a method of this kind where the crystalline material sample is a single crystal. It is well-known that diffraction of X-rays by a crystal occurs when Bragg's equation is fulfilled, λ=2*d*sin θ, where λ is the wavelength of the X-ray, d is the spacing of the crystal lattice planes causing diffraction, and θ (called the Bragg angle) is the angle between the X-Ray beam and the lattice plane. The source provides a polychromatic X-ray beam including many different wavelengths, which for any given position of the sample in relation to the source provides a high probability for actual diffraction from the single crystal. In addition the beam path is divergent and consequently at each point on the sample the X-rays impinge with a different Bragg angle, varying from θmin to θmax, and this variation range of the Bragg angle is determined by the geometry of the set-up, namely the distance from the source to the sample and the size of the sample in combination with the divergence of the X-ray beam. The article describes a focussing effect obtained when the detector is at a distance from the sample corresponding to the distance from the source to the sample while at the same time the diffracting planes are perpendicular to the surface of the single crystal. The focussing effect occurs in the scattering plane and causes the diffracted X-ray beam to hit the detector as a substantially two-dimensional line-shaped segment oriented perpendicular to the scattering plane.
U.S. Pat. No. 3,903,415 discloses diffraction measurements in a set-up using an X-ray source providing white (polychromatic) X-ray radiation. Pinhole diaphragms are located in the X-ray beam path to collimate the beam into a parallel beam before it reaches the sample. A lead plate is located behind the sample. The lead plate has a circular opening allowing X-ray radiation diffracted by the sample at a predetermined angle to pass on to a detector located behind the lead plate, whereas other X-ray radiation is blocked by the lead plate.
U.S. Pat. No. 5,491,738 discloses an X-ray diffraction apparatus having a beam source providing a collimated X-ray beam being preferably monochromatic. The non-collimated beam from the X-ray source is divergent, and a collimator with a pinhole makes the beam line-shaped and parallel before it reaches the sample. If the X-ray beam is polychromatic, then the detector is designed to measure the distribution of X-ray diffraction photons within one selected energy range, or within some selected energy ranges.
The article “X-ray diffraction contrast tomography: a novel technique for three-dimensional grain mapping of polycrystals. Part 1: direct beam case”, Journal of Applied Crystallography (2008), 41, 302-309 describes application of a monochrome synchrotron X-ray beam to illuminate a sample. With X-ray diffraction contrast tomography the grains of a polycrystalline material sample are imaged using an occasionally occurring diffraction contribution to the X-ray attenuation coefficient in the non-diffracted X-ray beam leaving the crystalline material sample. The analysis is thus using the information detected in the direct beam path. Each time a grain fulfils the Bragg diffraction condition a diffraction contrast occurs. The diffraction contrast appears on the detector behind the sample as an extinction spot caused by a local reduction of the transmitted beam intensity recorded on the detector. In the article, the three-dimensional grain shapes are reconstructed from a plurality of projections using algebraic reconstruction techniques (ART). The procedure for the three-dimensional grain shape reconstruction is based on spatial filtering criteria only, and the procedure can therefore be performed without analysing the grain orientations. With respect to grain orientations the article specifies that the intensity of the diffractions spots must be included in order to determine orientations, and even with integrated intensities several solutions may exist and choices have to be made. It is explained in the article that overlapping diffraction contrasts present a problem and that the sample consequently had to have only little grain orientation spread, grains of approximately the same size and tailored transverse sample dimensions in order to limit the probability of spot overlap.
Considerable efforts have been put into the development of techniques for three-dimensional grain mapping of polycrystalline materials. These techniques are utilizing monochromatic, parallel X-ray beams from a synchrotron facility and employ reconstruction algorithms of the kind known in tomography in order to provide a non-destructive characterization of a sample of polycrystalline material.
An example of utilizing monochromatic, parallel X-ray beams from a synchrotron facility is given in the article “Three-dimensional grain mapping by x-ray diffraction contrast tomography and the use of Friedel pairs in diffraction data analysis” by W. Ludwig et al., Review of Scientific Instruments, 80, 033905 (2009). The method used in this article is based on X-ray diffraction contrast tomography, where the grains of a polycrystalline material sample are imaged using a occasionally occurring diffraction contribution to the X-ray attenuation coefficient in the non-diffracted X-ray beam leaving the crystalline material sample. This analysis using the information detected in the direct beam path is supplemented with analysis of the diffracted beams, and in a full 360° rotation of the sample the Bragg angle is fulfilled a maximum of four times. Each set of lattice planes may thus give rise to four diffraction spots, which make up two pairs, where the spots in the pair are separated by a 180° rotation of the sample. The analysis relating to the pairs is based on the fact that the monochromatic X-ray beam has a known wavelength which simplifies the Bragg equation. The diffraction spots observed are of irregular shape and the intensity of the spots may be used to facilitate matching of the pairs. With respect to implementation in practise the article observes that using a computing cluster of 50 nodes, a data set comprising of 1000 grains could be analysed in one day. With a monochromatic, parallel X-ray beam it is thus a heavy processor task to obtain a result.